Answer
a. $4\%$
b. $8\%$
c. $12\%$
Work Step by Step
a. Given circumference $\frac{dC}{C}=\frac{0.4}{10}=4\%$, with $C=2\pi r$, we have $dC=2\pi dr$ and for the radius $\frac{dr}{r}=\frac{dC/2\pi}{C/2\pi}=\frac{dC}{C}=4\%$
b. For the surface area $S=4\pi r^2$, we have $dS=8\pi rdr$ and $\frac{dS}{S}=\frac{8\pi rdr}{4\pi r^2}=2\frac{dr}{r}=8\%$
c. For the volume $V=4\pi r^3/3$, we have $dV=4\pi r^2dr$ and $\frac{dV}{V}=\frac{4\pi r^2dr}{4\pi r^3/3}=3\frac{dr}{r}=12\%$
